Jeremy P. Erickson

Improved Tardiness Bounds for Global EDF

The Earliest Deadline First scheduling algorithm (EDF) is known to not be optimal under global scheduling on multiprocessor platforms. Results have been obtained that bound the maximum tardiness– the amount of time by which deadlines may be missed– of any feasible system of implicit-deadline sporadic tasks scheduled using global EDF. However, it is known that these bounds are not tight. In this paper, we derive an algorithm for obtaining tardiness bounds that are superior to previously known bounds. In contrast to prior algorithms, which compute a single tardiness bound for all the tasks in the system, our algorithm derives a separate tardiness bound for each task. Particularly upon task systems in which the parameters of the tasks are very dissimilar, our bounds are significantly better than prior bounds. Our algorithm also yields a simple sufficient test for the tardiness verification problem: given a task system with maximum acceptable tardiness bounds per task, is the system guaranteed to be scheduled by global EDF such that these tardiness constraints are not violated?

Fair lateness scheduling: reducing maximum lateness in G-EDF-like scheduling

In prior work on soft real-time (SRT) multiprocessor scheduling, tardiness bounds have been derived for a variety of scheduling algorithms, most notably, the global earliest-deadline-first (G-EDF) algorithm. In this paper, we devise G-EDF-like (GEL) schedulers, which have identical implementations to G-EDF and therefore the same overheads, but that provide better tardiness bounds. We discuss how to analyze these schedulers and propose methods to determine scheduler parameters to meet several different tardiness bound criteria. We employ linear programs to adjust such parameters to optimize arbitrary tardiness criteria, and to analyze lateness bounds (lateness is related to tardiness). We also propose a particular scheduling algorithm, namely the global fair lateness (G-FL) algorithm, to minimize maximum absolute lateness bounds. Unlike the other schedulers described in this paper, G-FL only requires linear programming for analysis. We argue that our proposed schedulers, such as G-FL, should replace G-EDF for SRT applications.

Algebraic cryptanalysis of SMS4: gröbner basis attack and SAT attack compared

The SMS4 block cipher is part of the Chinese WAPI wireless standard. This paper describes the specification and offers a specification for a toy version called simplified SMS4 (S-SMS4). We explore algebraic attacks on SMS4 and S-SMS4 using Grobner basis attacks on equation systems over GF(2) and GF(28), as well as attacks using a SAT solver derived from the GF(2) model. A comparison of SAT and Grobner basis attacks is provided.

Optimal semi-partitioned scheduling in soft real-time systems

Semi-partitioned real-time scheduling algorithms extend partitioned ones by allowing a (usually small) subset of tasks to migrate. The first such algorithm to be proposed was directed at soft real-time (SRT) sporadic task systems where bounded deadline tardiness is acceptable. That algorithm, called EDF-fm, has the desirable property that migrations are boundary-limited, i.e., they can only occur at job boundaries. However, it is not optimal because per-task utilization restrictions are required. In this paper, a new optimal semi-partitioned scheduling algorithm for SRT sporadic task systems is proposed that eliminates such restrictions. This algorithm, called EDF-os, preserves the boundary-limited property. In overhead-aware schedulability experiments presented herein, EDF-os proved to be better than all other tested alternatives in terms of schedulability in almost all considered scenarios. It also proved capable of ensuring very low tardiness bounds, which were near zero in most considered scenarios.

Tardiness bounds for global EDF with deadlines different from periods

The Earliest Deadline First (EDF) scheduling algorithm is known to be suboptimal for meeting all deadlines under global scheduling on multiprocessor platforms. However, EDF is an attractive choice for scheduling soft-real-time systems on multiprocessors. Previous work has demonstrated that the maximum tardiness is bounded, and has derived formulas for computing tardiness bounds, in EDF-scheduled real-time systems that can be modeled as collections of recurrent tasks modeled using the well-known implicit-deadline (Liu and Layland) task model. This research extends the applicability of previous techniques to systems that are modeled using the more general arbitrary sporadic task model. It also improves on prior work even for implicit-deadline systems. An algorithm is derived here that computes tardiness bounds in polynomial time. Previously, these bounds could only have been approximated in sub-exponential time.

Minimizing response times of automotive dataflows on multicore

Dataflow software architectures are prevalent in prototypes of advanced automotive systems, for both driver-assisted and autonomous driving. Safety constraints of these systems necessitate real-time performance guarantees. Automotive prototypes often ensure such constraints through over-provisioning and dedicated hardware; however, a commercially viable system must utilize as few low-cost multicore processors as possible to meet size, weight, and power constraints. In short, these platforms must do more with less. To this end, we develop cache-aware and overhead-cognizant scheduling techniques that lessen guaranteed response times without unnecessarily constraining platform utilization. We implement these techniques in PGMRT, a portable middleware framework for managing real-time dataflow applications on multicore platforms. The efficacy of our techniques is demonstrated through overhead-aware schedulability experiments and runtime observations. Results for our test platform show that cache-aware clustered scheduling outperforms naïve partitioned and global approaches in terms of schedulability and end-to-end response times of dataflows.

Reducing Tardiness under Global Scheduling by Splitting Jobs

Under current analysis, soft real-time tardiness bounds applicable to global earliest-deadline-first scheduling and related policies depend on per-task worst-case execution times. By splitting job budgets to create sub jobs with shorter periods and worst-case execution times, such bounds can be reduced to near zero for implicit-deadline sporadic task systems. However, doing so could potentially cause more preemptions and create problems for synchronization protocols. This paper analyzes this tradeoff between theory and practice by presenting an overhead-aware schedulability study pertaining to job splitting. In this study, real overhead data from a scheduler implementation in LITMUSRT was factored into schedulability analysis. This study shows that despite practical issues affecting job splitting, it can still yield substantial reductions in tardiness bounds for soft real-time systems.

Outstanding Paper Award: Fair Lateness Scheduling: Reducing Maximum Lateness in G-EDF-Like Scheduling

Existing research in soft real-time scheduling has focused on determining tardiness bounds given a scheduling algorithm. In this paper, we study lateness bounds, which are related to tardiness bounds, and propose a scheduling algorithm to minimize lateness bounds, namely the global fair lateness (G-FL) algorithm. G-FL is a G-EDF-like scheduler, but has lower maximum lateness bounds than GEDF. Due to its G-EDF-like nature, it can be used within existing systems that implement arbitrary-deadline G-EDF, and with existing synchronization protocols. Therefore, we argue that G-FL should replace G-EDF for SRT applications.

Response time bounds for G-EDF without intra-task precedence constraints

Prior work has provided bounds on the deadline tardiness that a set of sporadic real-time tasks may incur when scheduled using the global earliest-deadline-first (G-EDF) scheduling algorithm. Under the sporadic task model, it is necessary that no individual task overutilize a single processor and that the set of all tasks does not overutilize the set of all processors. In this work we generalize the task model by allowing jobs within a single task to run concurrently. In doing so we remove the requirement that no task overutilize a single processor. We also provide tardiness bounds that are better than those available with the standard sporadic task model.

Soft Real-Time Scheduling in Google Earth

Google Earth is a virtual globe that allows users to explore satellite imagery, terrain, 3D buildings, and geo-spatial content. It is available on a wide variety of desktop and mobile platforms, including Windows, Mac OS X, Linux, iOS, and Android. To preserve the sense of fluid motion through a 3D environment, the application must render at 60Hz. In this paper, we discuss the scheduling constraints of this application as a soft real-time scheduling problem where missed deadlines disrupt this motion. We describe a new scheduling implementation that addresses these problems. The diversity of hardware and software platforms on which Google Earth runs makes offline execution time analysis infeasible, so we discuss ways to predict execution time using on line measurement. We provide experimental results comparing different methods for predicting execution time. This new implementation is slated for inclusion in a future release of Google Earth.